My fence has block pillars instead of posts and so I've screwed battens to the blocks and then screwed the panels to that just using standard long wood screws. I would have thought you'll want to do something similar, although what you've made sounds pretty heavy to me. Is it? That might be a problem whatever you do.

I'd be inclined to rebate it as mentioned above or fix some timber that will slot into the grooves to the ends of the panel - presumably you would have to cut the panel down to accommodate the added timber.